Product, quotient and chain rules

Product, quotient and chain rules Quiz

Spec 4.2 · Edexcel International A Level Maths: Quiz

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5 questions, one answer each

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  1. 1. Differentiate y=xsin⁡xy=x\sin x.

    • A. cos⁡x\cos x
    • B. sin⁡x+xcos⁡x\sin x+x\cos x
    • C. xcos⁡x−sin⁡xx\cos x-\sin x
    • D. sin⁡x−xcos⁡x\sin x-x\cos x

  2. 2. Differentiate y=sin⁡xxy=\dfrac{\sin x}{x}.

    • A. xcos⁡x+sin⁡xx2\dfrac{x\cos x+\sin x}{x^{2}}
    • B. cos⁡x1\dfrac{\cos x}{1}
    • C. xcos⁡x−sin⁡xx2\dfrac{x\cos x-\sin x}{x^{2}}
    • D. sin⁡x−xcos⁡xx2\dfrac{\sin x-x\cos x}{x^{2}}

  3. 3. Differentiate y=(3x+1)5y=(3x+1)^{5}.

    • A. 5(3x+1)45(3x+1)^{4}
    • B. 3(3x+1)53(3x+1)^{5}
    • C. 15(3x+1)415(3x+1)^{4}
    • D. 15(3x+1)615(3x+1)^{6}

  4. 4. Differentiate y=sec⁡xy=\sec x.

    • A. sec⁡xtan⁡x\sec x\tan x
    • B. tan⁡x\tan x
    • C. −sec⁡xtan⁡x-\sec x\tan x
    • D. sec⁡2x\sec^{2}x

  5. 5. Differentiate y=excot⁡xy=e^{x}\cot x.

    • A. ex(cot⁡x+cosec⁡2x)e^{x}\left(\cot x+\operatorname{cosec}^{2}x\right)
    • B. excosec⁡2xe^{x}\operatorname{cosec}^{2}x
    • C. −excosec⁡2x-e^{x}\operatorname{cosec}^{2}x
    • D. ex(cot⁡x−cosec⁡2x)e^{x}\left(\cot x-\operatorname{cosec}^{2}x\right)

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